(i) a2+b2 = (2)2+(-2)2 = 4+4=8 [putting a=2,b=-2]
(ii) a2+ab+b2 = (2)2+(2)(-2)+(-2)2 = 4-4+4=4 [putting a=2,b=-2]
(iii)a2–b2 = (2)2-(-2)2 = 4-4=0 [putting a=2,b=-2]
If \( x, y \) are two positive integers such that \( x + y = 20 \) and the maximum value of \( x^3 y \) is \( k \) at \( x = a, y = \beta \), then \( \frac{k}{\alpha^2 \beta^2} = ? \)
Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30